Some important distributions of continuous random variables

23 Novembro 2015, 13:30 • Graça Leão Fernandes

The Uniform distribution:

- definition;

- probability density and cumulative distribution function;

- moment generating function - expected value and variance, coefficient of assymetry;

- probability integral transformation.

The Exponential distribution:

- relation with the Poisson Process;

- determination of the CDF and PDF based on a Poisson Process;

- expected value and its relationship with the intensity rate of a Poisson Process;

- variance;

- property of lack of memory.

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Distributions of discrete random variables: Bernoulli, binomial and Poisson

19 Novembro 2015, 15:30 • Graça Leão Fernandes

Exercises of chapter 4 nºs: 1, 2, 3, 5, 11, 13, 16, 17.

 

3rd mini test

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Some distributions of discrete random variables - The Poisson distribution

18 Novembro 2015, 15:30 • Graça Leão Fernandes

The Poisson distribution:

- Assumptions of a Poisson Process;

- Definition of a random variable that follows a Poisson distribution;

- Interpretation of the distribution parameter;

- Finding the pdf of a random variable following a Poisson distribution from the Binomial distribution;

- Aditivity theorem;

- Computing probabilities using calculators and tables;

- Examples.

 

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Discrete random variables distributions: Uniform discrete, Bernoulli and Binomial.

16 Novembro 2015, 13:30 • Graça Leão Fernandes

Discrete random variables distributions:

 - Uniform discrete: definition, probability function,moment generating function, moments about the origin and about the mean.

 - Bernoulli: definition, probability function,moment generating function, moments about the origin and about the mean.

 -  Binomial: definition, probability function,moment generating function, moments about the origin and about the mean. Computing probabilities using the calculator or the table.

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Product moments about the origin and the mean for discrete and continuous two dimensional random variables. Covariance and correlation coefficient. conditional expected values.

12 Novembro 2015, 15:30 • Graça Leão Fernandes

Exercises from Chapter 3 nºs: 12, 14, 17, 19, 23

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